1
$\begingroup$

This question asks about how to intersect a ray with a bezier triangle: Intersect Ray (Line) vs Quadratic Bezier Triangle

What would happen if we had a bezier triangle that had scalars for control points, so they only controlled the height of each point on a triangle?

Would it be much easier then to find where a line intersected it?

Unfortunately I'm not sure where to even start, other than this equation, the explicit quadratic Bezier triangle! Anyone able to help me out?

$y = P_0S^2+2P_1ST+2P_2SU+P_3T^2+2P_4TU+P_5U^2$

$S,T,U$ are the barycentric coordinates of the triangle and $P_i$ are the scalar control points.

How would I go about finding where a line intersected with such an object, if it did at all?

$\endgroup$
1
$\begingroup$

This is much easier than the general case you asked about before.

You can eliminate $S$, $T$, $U$, and get the equation of the triangular patch in the implicit form $f(x,y,z) = 0$. In fact, the function $f$ will have degree 2, which means that the patch is actually just a portion of a quadric surface. Intersecting a line with a quadric surface is fairly straightforward --- you just have to solve a quadratic equation.

$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged or ask your own question.